arxiv: 2604.12222 · v1 · submitted 2026-04-14 · ❄️ cond-mat.mtrl-sci · astro-ph.EP

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Fe-H melting curve below 3 GPa: Implications for hydrogen in the lunar core

Jun Takeshita , Kei Hirose , Suyu Fu , Fumiya Sakai , Koutaro Hikosaka

Authors on Pith no claims yet

Pith reviewed 2026-05-10 16:20 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci astro-ph.EP

keywords Fe-H systemlunar corehydrogen solubilitymelting curvedensity deficithigh-pressure experimentsynchrotron XRDplanetary cores

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The pith

Hydrogen dissolves in liquid iron below 3 GPa and reaches levels that can explain the Moon's core density deficit.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows through melting experiments that the Fe-H melting curve drops markedly below the pure-iron curve starting at pressures under 1 GPa, proving that hydrogen enters molten iron in noticeable amounts even at low pressure. Solubility increases with pressure, reaching roughly 0.9 weight percent at 3.6 GPa. Extrapolation to the 5 GPa conditions of the lunar core suggests about 1.2 weight percent hydrogen, which lowers the density of the liquid by 9 percent. This reduction is large enough to account for the entire observed density shortfall of the lunar core relative to pure iron, depending on the exact value from seismic models. A reader would care because it overturns the assumption that hydrogen plays no role in the cores of small bodies like the Moon and supplies a straightforward explanation for their interior structure.

Core claim

The central claim is that hydrogen is incorporated into liquid iron even below 1 GPa under H2-saturated conditions, with the solubility rising from about 0.9 wt% at 3.6 GPa to an estimated 1.2 wt% at 5 GPa; this incorporation depresses the melting curve and produces a 9% density reduction in the liquid that can fully explain the lunar core's density deficit with respect to iron, as derived from diffuse scattering signals in the X-ray data.

What carries the argument

High-pressure melting experiments on the Fe-H system under H2-saturated conditions, combined with synchrotron X-ray diffraction measurements that track melting-curve depression and extract liquid density from diffuse scattering signals.

If this is right

The Fe-H melting curve lies below the pure-Fe curve at all pressures from 1.0 to 3.3 GPa.
Hydrogen solubility in liquid iron increases steadily with pressure in this range.
At lunar-core pressure the liquid contains enough hydrogen to lower its density by 9 percent.
This density drop can match the full observed deficit in the Moon's core depending on the seismological density value adopted.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Core-formation models for the Moon and similar small bodies must now include hydrogen partitioning at pressures well below 3 GPa.
The same solubility trend may operate in other low-pressure metallic cores such as those inferred for Mercury or differentiated asteroids.
Seismic velocity profiles of the lunar core could be tested against predictions that include 1.2 wt% hydrogen rather than other candidate light elements.

Load-bearing premise

The measured solubility trend up to 3.6 GPa can be extrapolated linearly to 5 GPa and that hydrogen is the main or only light element responsible for the observed density deficit.

What would settle it

A direct measurement of hydrogen concentration in liquid iron at 5 GPa that yields less than 0.8 wt% H or a revised lunar-core density estimate from seismology that leaves no room for a 9% reduction.

read the original abstract

It has been assumed that hydrogen is negligibly incorporated into core-forming metals below $\sim$3 GPa, and therefore the presence of hydrogen in iron cores of small terrestrial bodies including the moon has not been considered. Here we performed high-pressure melting experiments on the Fe-H system under H$_2$-saturated conditions, combined with synchrotron X-ray diffraction (XRD) measurements. Results demonstrate substantial depression of the Fe-H melting curve compared to that for Fe at 1.0-3.3 GPa, indicating that hydrogen is incorporated into liquid iron even at low pressures less than 1 GPa and the solubility is enhanced with increasing pressure. Based on the density of liquid Fe-H derived from diffuse scattering signal in XRD data, we found that the solubility of hydrogen in liquid iron is about 0.9 wt% at 3.6 GPa and likely enhanced to 1.2 wt% at 5 GPa corresponding to lunar core conditions. The 1.2 wt% H causes 9 % density reduction, which might fully explain the observed density deficit of the lunar core with respect to iron, depending on the density estimate from seismological data.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper gives new experimental melting points and solubility estimates for Fe-H below 3 GPa that were missing before, but the 0.9 wt% H figure at 3.6 GPa and the lunar-core conclusion rest on converting diffuse XRD scattering to density.

read the letter

The main thing here is the new melting-curve data. They ran Fe-H experiments under H2-saturated conditions from about 1 to 3.3 GPa and saw clear depression of the melting point compared with pure Fe. That directly shows hydrogen goes into the liquid even at these low pressures, where people had assumed it was negligible. The synchrotron XRD part adds density estimates from the diffuse scattering, leading to their claim of roughly 0.9 wt% H at 3.6 GPa and an extrapolation to 1.2 wt% at 5 GPa. If that holds, it could close the lunar core density gap with a 9% reduction. That is the useful extension of prior high-pressure work into the regime relevant for the Moon and other small bodies. The experiments themselves look like a straightforward application of established high-pressure techniques, and the qualitative result on incorporation is straightforward. The quantitative step is the softer part. Turning the diffuse signal into a precise hydrogen concentration requires a clean reference density for pure liquid Fe, good background handling, and an assumption about how H mixes in. Any systematic offset in those steps scales straight into the 0.9 wt% number and the 9% density drop. The paper also extrapolates beyond the measured range to 5 GPa, which adds another layer of uncertainty. The abstract does not spell out error bars or data-selection criteria, so it is hard to judge how robust the conversion really is without the full methods and raw patterns. This is the kind of work planetary scientists who model small-body cores will want to see. The new low-pressure points are worth having even if the exact solubility needs tighter error bars. It is not a load-bearing flaw, just the usual place where these experiments can be sensitive. I would send it to peer review so the methods and data tables get proper scrutiny.

Referee Report

2 major / 3 minor

Summary. The paper reports synchrotron XRD experiments on Fe-H melting under H2-saturated conditions at 1.0-3.6 GPa. It shows substantial depression of the melting curve relative to pure Fe, interpreted as evidence for H incorporation into liquid iron even below 1 GPa, with solubility increasing with pressure. Density of the liquid Fe-H alloy is extracted from the diffuse scattering signal; this yields an estimated solubility of ~0.9 wt% H at 3.6 GPa that is extrapolated to ~1.2 wt% H at 5 GPa. The authors conclude that this H content produces a ~9% density reduction that could fully account for the lunar core density deficit relative to pure iron, depending on seismological constraints.

Significance. If the quantitative solubility values and density conversion hold, the work would revise the long-standing assumption that H incorporation into core-forming metals is negligible below ~3 GPa and would supply a plausible single-light-element explanation for the lunar core density deficit. The combination of in-situ melting-curve determination with diffuse-scattering density measurement is a methodological strength that could be extended to other Fe-light-element systems.

major comments (2)

[Results (diffuse scattering density derivation)] Diffuse-scattering density section (results describing liquid Fe-H density extraction): the conversion of the diffuse XRD signal to liquid density and then to 0.9 wt% H at 3.6 GPa rests on an assumed reference density for pure liquid Fe, a specific structure-factor extraction procedure, and a linear mixing rule or partial-molar-volume value for H. No explicit equation, sensitivity analysis, or propagated uncertainties on background subtraction and peak fitting are provided; systematic bias in any of these steps scales directly into the reported wt% value and the subsequent 9% density-reduction claim.
[Discussion (extrapolation to 5 GPa)] Extrapolation paragraph (discussion of lunar-core conditions): the step from the measured 0.9 wt% at 3.6 GPa to 1.2 wt% at 5 GPa is presented without a fitted functional form, additional data points, or thermodynamic model. Because the 9% density reduction and the “might fully explain” conclusion for the lunar core depend on this extrapolated number, the central planetary implication is sensitive to the extrapolation method and to the assumption that H2-saturated laboratory conditions match the lunar core environment.

minor comments (3)

[Abstract] The abstract states experiments were performed at 1.0-3.3 GPa yet quotes a 3.6 GPa solubility value; clarify whether the 3.6 GPa datum comes from an additional run or from interpolation.
[Methods / Figure captions] Figure captions and text should explicitly state the pressure calibration method, temperature measurement uncertainty, and criteria used to identify the onset of melting from the XRD patterns.
[Results] The manuscript would benefit from a short comparison table of the new melting points against existing Fe and Fe-H data sets at overlapping pressures.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful and constructive review. The comments highlight important areas where the methodological details and the basis for the planetary implications can be strengthened. We address each major comment below and will revise the manuscript accordingly.

read point-by-point responses

Referee: Diffuse-scattering density section (results describing liquid Fe-H density extraction): the conversion of the diffuse XRD signal to liquid density and then to 0.9 wt% H at 3.6 GPa rests on an assumed reference density for pure liquid Fe, a specific structure-factor extraction procedure, and a linear mixing rule or partial-molar-volume value for H. No explicit equation, sensitivity analysis, or propagated uncertainties on background subtraction and peak fitting are provided; systematic bias in any of these steps scales directly into the reported wt% value and the subsequent 9% density-reduction claim.

Authors: We agree that additional documentation is required for the density derivation. In the revised manuscript we will insert the explicit equations relating the extracted structure factor to liquid density, specify the reference density adopted for pure liquid Fe, the partial-molar-volume value used for hydrogen, and the precise background-subtraction and peak-fitting protocols. We will also add a sensitivity analysis that propagates uncertainties from each step into the final wt% H and density-reduction values. These additions will allow readers to evaluate the robustness of the reported 0.9 wt% H at 3.6 GPa. revision: yes
Referee: Extrapolation paragraph (discussion of lunar-core conditions): the step from the measured 0.9 wt% at 3.6 GPa to 1.2 wt% at 5 GPa is presented without a fitted functional form, additional data points, or thermodynamic model. Because the 9% density reduction and the “might fully explain” conclusion for the lunar core depend on this extrapolated number, the central planetary implication is sensitive to the extrapolation method and to the assumption that H2-saturated laboratory conditions match the lunar core environment.

Authors: The 1.2 wt% figure at 5 GPa is an estimate based on the clear pressure-dependent increase in solubility already evident in the melting-curve data between 1 and 3.6 GPa together with the single density-derived point at 3.6 GPa. We acknowledge that a full thermodynamic model cannot be constructed from the present data set alone. In revision we will (i) fit a simple linear trend to the available solubility estimates, (ii) report the formal uncertainty on the extrapolated value, and (iii) expand the discussion of laboratory versus lunar-core conditions, explicitly noting differences in sulfur content and oxygen fugacity. The conclusion will be rephrased to emphasize that the data indicate hydrogen could account for a substantial fraction of the density deficit, subject to these uncertainties and to seismological constraints. revision: partial

Circularity Check

0 steps flagged

No circularity: solubility derived from independent XRD density measurements

full rationale

The paper's key quantitative result (0.9 wt% H at 3.6 GPa) is obtained by measuring the diffuse scattering signal in synchrotron XRD to determine liquid Fe-H density, then applying a standard density-deficit to concentration conversion. This step uses external reference densities for pure Fe and a linear mixing assumption but does not define the output in terms of the input by construction, nor does it fit parameters to the lunar-core density deficit and relabel them as predictions. Melting-curve depression provides only supporting qualitative evidence. No self-citations are invoked as load-bearing uniqueness theorems or ansatzes for the central derivation, and the extrapolation to 5 GPa is a simple pressure scaling rather than a self-referential fit. The chain remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests primarily on experimental data rather than theoretical derivations. Key assumptions include the representativeness of lab conditions for the lunar core and the attribution of density changes solely to hydrogen.

free parameters (1)

hydrogen solubility at 5 GPa
Projected value based on trend from data up to 3.6 GPa rather than direct measurement at lunar core pressure.

axioms (2)

domain assumption Lunar core pressure is approximately 5 GPa
Used to extrapolate solubility and density effects to lunar conditions.
domain assumption Density reduction is due solely to hydrogen incorporation
Assumes no contribution from other light elements or effects in the core.

pith-pipeline@v0.9.0 · 5529 in / 1564 out tokens · 73306 ms · 2026-05-10T16:20:43.727481+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

10 extracted references · 6 canonical work pages

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Here we performed high-pressure melting experiments on the Fe-H system under H2-saturated conditions, combined with synchrotron X-ray diffraction (XRD) measurements

Department of Earth and Planetary Sciences, Institute of Science Tokyo, Tokyo 150-8551, Japan * Corresponding author (email: kei@eps.s.u-tokyo.ac.jp) Abstract It has been assumed that hydrogen is negligibly incorporated into core-forming metals below ~3 GPa, and therefore the presence of hydrogen in iron cores of small terrestrial bodies including the moo...

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The increase in the hydrogen abundance in liquid with increasing pressure is supported by the shift of the first-peak position in structure factor S(Q) (Fig

and then obtained its hydrogen abundance considering the volume expansion by hydrogen; hydrogen concentration in liquid FeHx increased from x = 0.14 at 1.0 GPa to 0.48 at 3.6 GPa. The increase in the hydrogen abundance in liquid with increasing pressure is supported by the shift of the first-peak position in structure factor S(Q) (Fig. S-1). Since experim...

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(Fig. 2). It could be a consequence of a rapid increase in the hydrogen solubility into fcc Fe (Fig. S-2), which is inferred from the formation of stoichiometric FeH above that pressure at 300 K (Badding et al., 1991). Possible hydrogen abundance in the lunar core The present experiments demonstrate the depression of melting temperature of iron by ~240 K ...

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We can also calculate the possible hydrogen content in the lunar core based on its metal-silicate partitioning under core formation conditions

suggest that the hydrogen solubility limit in liquid iron may be x = 0.37 and 0.65 in FeHx (0.7 and 1.2 wt% H) at 2.8 and 5 GPa, respectively. We can also calculate the possible hydrogen content in the lunar core based on its metal-silicate partitioning under core formation conditions. Water concentration in the bulk silicate moon (BSM) has been estimated...

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#_%&&%'()*%=(3×𝑇!

(red line). The grey line represents the melting curve of pure Fe. Figure 3 The hydrogen contents in coexisting solid fcc and liquid phases in this study. The theoretical predictions of those in liquid by Stoutenburg et al. (2026) at 1500 K are also shown. Figure 4 Density of liquid FeHx as a function of hydrogen concentration at 5 GPa and 1700 K. The den...

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Figure S-4 Determination of liquid density from diffuse scattering using the analytical method developed by Kuwayama et al

and carbon-free metal composition. Figure S-4 Determination of liquid density from diffuse scattering using the analytical method developed by Kuwayama et al. (2020). (a) The structure factor S(Q), (b) reduced interference function f(Q), (c) distribution function F(r), and (d) radial distribution function g(r) (Q is momentum transfer). The black lines rep...

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https://doi.org/10.1038/s41467-021-22035-0 Tagawa, S., Helffrich, G., Hirose, K., Ohishi, Y. (2022) High-pressure melting curve of FeH: Implications for eutectic melting between Fe and non-magnetic FeH. Journal of Geophysical Research: Solid Earth 127, e2022JB024365. https://doi.org/10.1029/2022JB024365 Tateno, S., Komabayashi, T., Hirose, K., Hirao, N., ...

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